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Linear Time Algorithms for Some NP-Complete Problems on (P 5,Gem)-Free Graphs

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Fundamentals of Computation Theory (FCT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2751))

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Abstract

A graph is (P 5,gem)-free, when it does not contain P 5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P 4) as an induced subgraph.

Using a characterization of (P 5,gem)-free graphs by their prime graphs with respect to modular decomposition and their modular decomposition trees [6], we obtain linear time algorithms for the following NP-complete problems on (P 5,gem)-free graphs: Minimum Coloring, Maximum Weight Stable Set, Maximum Weight Clique, and Minimum Clique Cover.

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Author information

Authors and Affiliations

  1. Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508, TB, Utrecht, The Netherlands

    Hans Bodlaender

  2. Fachbereich Informatik, Universität Rostock, A.-Einstein-Str. 21, 18051, Rostock, Germany

    Andreas Brandstädt

  3. Laboratoire d’Informatique Théorique et Appliquée, Université de Metz, 57045 Cedex 01, Metz, France

    Dieter Kratsch & Michaël Rao

  4. Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, 37235, USA

    Jeremy Spinrad

Authors
  1. Hans Bodlaender
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  2. Andreas Brandstädt
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  3. Dieter Kratsch
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  4. Michaël Rao
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  5. Jeremy Spinrad
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Bengt J. Nilsson

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Bodlaender, H., Brandstädt, A., Kratsch, D., Rao, M., Spinrad, J. (2003). Linear Time Algorithms for Some NP-Complete Problems on (P 5,Gem)-Free Graphs. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_7

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  • DOI: https://doi.org/10.1007/978-3-540-45077-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40543-6

  • Online ISBN: 978-3-540-45077-1

  • eBook Packages: Springer Book Archive

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